U.S. patent application number 10/990715 was filed with the patent office on 2005-06-16 for non-linear control of a balancing vehicle.
This patent application is currently assigned to DEKA Products Limited Partnership. Invention is credited to Amsbury, Burl, Field, J. Douglas, Kerwin, John M., Morrell, John B., Pompa, Johnathan B..
Application Number | 20050126832 10/990715 |
Document ID | / |
Family ID | 34656807 |
Filed Date | 2005-06-16 |
United States Patent
Application |
20050126832 |
Kind Code |
A1 |
Amsbury, Burl ; et
al. |
June 16, 2005 |
Non-linear control of a balancing vehicle
Abstract
A class of transporters for carrying an individual over ground
having a surface that may be irregular. Various embodiments have a
motorized drive, mounted to the ground-contacting module that
causes operation of the transporter in an operating position that
is unstable with respect to tipping when the motorized drive
arrangement is not powered. Methods of controlling the transporter
are described that allow the dynamic behavior of the transporter to
more closely match preferences of a rider. These methods include
providing preferential responsiveness to change in pitch angles and
pitch rates.
Inventors: |
Amsbury, Burl; (Boulder,
CO) ; Field, J. Douglas; (Bedford, NH) ;
Kerwin, John M.; (Manchester, NH) ; Morrell, John
B.; (Bedford, NH) ; Pompa, Johnathan B.; (La
Jolla, CA) |
Correspondence
Address: |
BROMBERG & SUNSTEIN LLP
125 SUMMER STREET
BOSTON
MA
02110-1618
US
|
Assignee: |
DEKA Products Limited
Partnership
Manchester
NH
|
Family ID: |
34656807 |
Appl. No.: |
10/990715 |
Filed: |
November 17, 2004 |
Related U.S. Patent Documents
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Application
Number |
Filing Date |
Patent Number |
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10990715 |
Nov 17, 2004 |
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10460053 |
Jun 12, 2003 |
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6827163 |
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60388723 |
Jun 14, 2002 |
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Current U.S.
Class: |
180/7.1 |
Current CPC
Class: |
B60L 2240/423 20130101;
B60L 2240/547 20130101; B60L 2240/14 20130101; B60L 2220/46
20130101; B60L 2240/421 20130101; B60L 2240/545 20130101; B62K
11/007 20161101; B60L 2260/34 20130101; B60L 2240/463 20130101;
Y02T 10/64 20130101; B62K 17/00 20130101; Y02T 10/72 20130101; B60L
2200/16 20130101; B60L 15/2045 20130101; B60L 2240/549 20130101;
B60L 2240/461 20130101; B60L 15/20 20130101 |
Class at
Publication: |
180/007.1 |
International
Class: |
B62D 057/036; B62D
057/032; B62D 057/00; B62D 057/024; B62D 057/028 |
Claims
What is claimed is:
1. A device for carrying a user, the device comprising: a. a
platform which supports a payload including the user, b. a
ground-contacting module, mounted to the platform, including at
least one ground-contacting member, characterized by a ground
contact region, and defining a fore-aft plane; c. a motorized drive
arrangement, coupled to the ground-contacting module; the drive
arrangement, ground-contacting module and payload constituting a
system being unstable with respect to tipping in at least the
fore-aft plane when the motorized drive is not powered, the system
characterized by a pitch angle offset from a specified pitch angle
and a pitch rate offset from a specified pitch rate; and d. a
control loop in which the motorized drive arrangement is included,
for dynamically maintaining stability of the system in the fore-aft
plane by operation of the motorized drive arrangement in such a
manner that a drive command supplied to the motorized drive
arrangement includes a contribution related to the pitch angle
offset multiplied by a first gain wherein the first gain is a
function of the instantaneous pitch of the device.
Description
[0001] The present application is a continuation application of
co-pending application Ser. No. 10/460,053, filed Jun. 12, 2003,
which claimed priority from provisional application, Ser. No.
60/388,723, attorney docket 1062/C84, filed Jun. 14, 2002, as does
the present application. Parent application Ser. No. 10/460,053
claimed priority from other applications which are listed hereunder
and which are incorporated by reference, however the present
application does not claim priority therefrom.
[0002] Parent application Ser. No. 10/460,053 was a
continuation-in-part application of co-pending application Ser. No.
09/325,976, attorney docket 1062/B99, filed Jun. 4, 1999, which was
a continuation in part of U.S. application Ser. No. 08/479,901,
filed Jun. 7, 1995, now issued as U.S. Pat. No. 5,975,225, which
was a continuation in part of U.S. application Ser. No. 08/384,705,
filed Feb. 3, 1995, now issued as U.S. Pat. No. 5,971,091, which
was a continuation in part of U.S. application Ser. No. 08/250,693,
filed May 27, 1994, now issued as U.S. Pat. No. 5,701,965.
TECHNICAL FIELD AND BACKGROUND ART
[0003] The present invention pertains to transporters and methods
for transporting individuals, and more particularly to balancing
transporters and methods for transporting individuals over ground
having a surface that may be irregular.
[0004] A wide range of transporters and methods are known for
transporting human subjects. Typically, such transporters rely upon
static stability, being designed so as to be stable under all
foreseen conditions of placement of their ground-contacting
members. Thus, for example, the gravity vector acting on the center
of gravity of an automobile passes between the points of ground
contact of the automobile's wheels, the suspension keeping all
wheels on the ground at all times, and the automobile is thus
stable. Another example of a statically stable transporter is the
stair-climbing transporter described in U.S. Pat. No. 4,790,548
(Decelles et al.).
SUMMARY OF THE INVENTION
[0005] In an embodiment of the invention, a transporter is provided
for carrying a user. The transporter includes:
[0006] a platform which supports a payload including the user,
[0007] a ground-contacting module, mounted to the platform,
including at least one ground-contacting member, characterized by a
ground contact region, and defining a fore-aft plane;
[0008] a motorized drive arrangement, coupled to the
ground-contacting module; the drive arrangement, ground-contacting
module and payload constituting a system being unstable with
respect to tipping in at least the fore-aft plane when the
motorized drive is not powered, the system characterized by a pitch
angle offset from a specified pitch angle and a pitch rate offset
from a specified pitch rate; and
[0009] a control loop in which the motorized drive arrangement is
included, for dynamically maintaining stability of the system in
the fore-aft plane by operation of the motorized drive arrangement
so that the net torque experienced by the system about the region
of contact with the surface causes a specified acceleration of the
system, the net torque including a contribution related to the
pitch angle offset multiplied by a first gain wherein the first
gain is a function of at least one of an orientation and a
displacement of the device.
[0010] In another embodiment of the invention, a balancing
transporter is provided. The transporter is characterized by an
instantaneous displacement and orientation. The transporter
includes a motorized drive for propelling the transporter; and a
control loop in which the motorized drive arrangement is included,
for dynamically maintaining stability of the system in the fore-aft
plane by operation of the motorized drive arrangement so that the
net torque experienced by the system about the region of contact
with the surface causes a specified acceleration of the system, the
net torque including a contribution functionally related to at
least one of the pitch angle, pitch rate, wheel position and wheel
velocity, wherein the functional relation varies with at least one
of an orientation and a displacement of the device.
[0011] In another embodiment of the invention, a method is provided
for carrying a payload including a user with a transporter. The
method comprises providing a transporter including:
[0012] a platform which supports a payload including the user,
[0013] a ground-contacting module, mounted to the platform,
including at least one ground-contacting member, characterized by a
ground contact region and a fore-aft plane;
[0014] a motorized drive arrangement, coupled to the
ground-contacting module; the drive arrangement, ground-contacting
module and payload constituting a system being unstable with
respect to tipping in at least the fore-aft plane when the
motorized drive is not powered, the system characterized by a pitch
angle offset from a specified pitch angle and a pitch rate offset
from a specified pitch rate; and causing the motorized drive to
operate the ground-contacting module using a control loop in which
the motorized drive arrangement is included, for dynamically
maintaining stability of the system in the fore-aft plane by
operation of the motorized drive arrangement so that the net torque
experienced by the system about the region of contact with the
surface causes a specified acceleration of the system. The net
torque includes
[0015] a contribution related to the pitch angle offset multiplied
by a first gain K.sub.1' when the pitch angle offset is greater
than or equal to zero and to the pitch angle offset multiplied by a
second gain K.sub.1" when the pitch angle offset is less than zero;
and
[0016] a contribution related to the pitch rate offset multiplied
by a third gain K.sub.2'; when the pitch rate offset is greater
than or equal to zero, and to the pitch rate offset multiplied by a
fourth gain K.sub.2" when the pitch rate offset is less than
zero,
[0017] wherein at least one of a first gain pair consisting of
K.sub.1' and K.sub.1" and a second gain pair consisting of K.sub.2'
and K.sub.2" are unequal.
[0018] In a specific embodiment of the preceding embodiment of the
invention, the magnitude of K.sub.1' is less than the magnitude of
K.sub.1". In a further specific embodiment, K.sub.2' equals
K.sub.2".
[0019] Embodiments of the invention advantageously allow the
response of the transporter to be tailored to rider
preferences.
BRIEF DESCRIPTION OF THE DRAWINGS
[0020] The foregoing features of the invention will be more readily
understood by reference to the following detailed description,
taken with reference to the accompanying drawings, in which:
[0021] FIG. 1 is a side view of a personal transporter lacking a
stable static position, in accordance with a preferred embodiment
of the present invention, for supporting or conveying a subject who
remains in a standing position thereon;
[0022] FIG. 2 is a perspective view of a further personal
transporter lacking a stable static position, in accordance with an
alternate embodiment of the present invention;
[0023] FIG. 3 illustrates the control strategy for a simplified
version of FIG. 1 to achieve balance using wheel torque;
[0024] FIG. 4 illustrates diagrammatically the operation of
joystick control of the wheels of the embodiment of FIG. 1;
[0025] FIG. 5 is a block diagram showing generally the nature of
sensors, power and control with the embodiment of FIG. 1;
[0026] FIG. 6 is a block diagram providing detail of a driver
interface assembly;
[0027] FIG. 7 is a schematic of the wheel motor control during
balancing and normal locomotion, in accordance with an embodiment
of the present invention;
[0028] FIG. 8 shows an illustrative diagram of an idealized
balancing transporter with a rigid wheel in motion at a constant
velocity across a flat surface; and
[0029] FIG. 9 illustrates non-linear gains for a transporter.
DETAILED DESCRIPTION OF SPECIFIC EMBODIMENTS
[0030] The subject matter of this application is related to U.S.
Pat. Nos. 5,701,965; 5,971,091; 5,791,425; 6,302,230; and U.S.
patent application Ser. No. 09/687,789, attorney's docket 1062/C40,
"Transporter Improvements," filed Oct. 13, 2000, which are all
incorporated herein by reference in their entirety. The subject
matter of this application is also related to the following U.S.
provisional patent applications: "Speed Limit Determination for a
Balancing Transporter," Attorney's Docket No. 1062/C67, Ser. No.
60/388,845; "Gain Scheduling in Control of a Balancing
Transporter," ser. No. 60/388,723, Attorney's Docket No. 1062/C84;
"Method and Device for Battery Charge Equalization," Attorney's
Docket No. 1062/C88; ser. No. 60/388,986; and "Speed Limiter for a
Balancing Transporter," Attorney's Docket No. 1062/C94; ser. No.
60/389,134, all filed on Jun. 14, 2002, all of which are
incorporated herein by reference in their entirety.
[0031] An alternative to operation of a statically stable
transporter is that dynamic stability may be maintained by action
of the user, as in the case of a bicycle or motorcycle or scooter,
or, in accordance with embodiments of the present invention, by a
control loop, as in the case of the human transporter described in
U.S. Pat. No. 5,701,965. The invention may be implemented in a wide
range of embodiments. A characteristic of many of these embodiments
is the use of a pair of laterally disposed ground-contacting
members to suspend the subject over the surface with respect to
which the subject is being transported. The ground or other
surface, such as a floor, over which a transporter in accordance
with the invention is employed may be referred to generally herein
as the "ground." The ground-contacting members are typically
motor-driven. In many embodiments, the configuration in which the
subject is suspended during locomotion lacks inherent stability at
least a portion of the time with respect to a vertical in the
fore-aft plane but is relatively stable with respect to a vertical
in the lateral plane. Stability, as defined below, means that in
response to a perturbation a stable device will tend towards its
unperturbed state.
[0032] Some embodiments of the invention invoke the concept of
primary wheels. The term "primary wheels," as used in this
description and in any appended claims, refers to a minimum set of
a transporter's wheels on which the transporter is capable of
operating stably. More generally, the term "primary
ground-contacting members" allows for a more general class of
members, that includes but is not limited to wheels. Hence, as used
in this description and in any appended claims, "primary
ground-contacting members" refers to a minimum set of a
transporter's ground-contacting members on which the transporter is
capable of operating stably. Other ground-contacting members may
include, without limitation: arcuate sections of a wheel, clusters
of wheels, treads, etc.
[0033] In various embodiments of the invention, fore-aft stability
may be achieved by providing a control loop, in which one or more
motors are included, for operation of a motorized drive in
connection with the ground-contacting members. As described below,
a pair of ground-contacting members may, for example, be a pair of
wheels or a pair of wheel clusters. In the case of wheel clusters,
each cluster may include a plurality of wheels. Each
ground-contacting member, however, may instead be a plurality
(typically a pair) of axially adjacent, radially supported and
rotatably mounted arcuate elements. In these embodiments, the
ground-contacting members are driven by the motorized drive in the
control loop in such a way as to maintain, when the transporter is
not in locomotion, the center of mass of the transporter above the
region of contact of the ground-contacting members with the ground,
regardless of disturbances and forces operative on the
transporter.
[0034] A ground-contacting member typically has a "point"
(actually, a region) of contact or tangency with the surface over
which the transporter is traveling or standing. Due to the
compliance of the ground-contacting member, the "point" of contact
is actually an area, where the region of contact may also be
referred to as a contact patch. The weight of the transporter is
distributed over the contact region, giving rise to a distribution
of pressures over the region, with the center of pressure displaced
forward during forward motion. The distribution of pressures is a
function both of the composition and structure of the wheel, the
rotational velocity of the wheel, the torque applied to the wheel,
and thus of the frictional forces acting on the wheel.
[0035] A force in the direction of motion is required to overcome
rolling friction (and other frictional forces, including air
resistance). Gravity may be used, in accordance with preferred
embodiments of the invention, to provide a torque about the point
of contact with the surface in a direction having a component in
the sense of desired motion. Referring to FIG. 8, to illustrate
these principles, a diagram is shown of the forces acting on a
transporter that locomotes with constant velocity v on a single
wheel over a flat surface. The principles now discussed may readily
be generalized to operation on a sloped surface and to accommodate
any other external forces that might be present. Wheel 160 of
radius R.sub.w rotates with respect to chassis 162 about axle 164
and contacts the underlying surface at point P. For purposes of
illustration only, it is assumed that wheel 160 contacts the
surface at a point.
[0036] The wheel is driven with respect to the transporter by a
torque T (supplied by a motor, for example) which in turn creates a
reaction torque -T on the transporter. Since the torque acts about
the axle 164, the reaction torque corresponds to a force F.sub.b
acting at the center of gravity (CG) of the system, including the
transporter and payload, where F.sub.b=T/R.sub.CG, where R.sub.CG
is the distance between the axle and the CG of the system. The line
170 from the CG to point P is at an angle .theta..sub.s relative to
the vertical 172.
[0037] The rolling friction, f, acting on the wheel at point P, is
proportional to the velocity v of the rim of the wheel, with the
proportionality expressed as f=.mu.v. For constant velocity to be
maintained, this force f must be exactly canceled. Consequently,
with gravity providing the force, the condition that must be
satisfied is:
F.sub.b cos .theta..sub.s=f.sub.b, (Eqn. 1)
[0038] where f.sub.b is the component of the reaction force acting
transverse to axis 174 between the CG and point P. In order to
prevent the transporter from falling, a stability condition must
also exist, namely that no net force acts on the CG in a direction
transverse to line 170, i.e., there is no net torque about the
point of contact P during motion at constant velocity (i.e., in an
inertial frame of reference where the point P is fixed). This
condition may be expressed as:
F.sub.g sin .theta..sub.s=f.sub.b, (Eqn. 2)
[0039] where F.sub.g sin .theta..sub.s is the "tipping" component
of gravity, and f.sub.b is the counter-tipping component of the
reactive force on the transporter caused by wheel rotation
(f.sub.b=F.sub.b cos .theta.), and where .theta. is the angle shown
line 170 and line 174.
[0040] Eqns. 1 and 2 may be combined to yield F.sub.g sin
.theta..sub.s cos .theta..sub.s=f=.mu.v, thus, in the limit of
small angles (where sin .theta. is approximately .theta.),
.theta.s=(.mu./F.sub.g)v, (Eqn. 3)
[0041] showing that increasing velocity requires increased lean to
overcome the effects of friction. Additionally, a control loop that
imposes stability on the system will respond to an increased lean
by increasing velocity of the system. While the preceding
discussion assumed constant velocity, additional lean beyond that
required to overcome the effects of friction will result in
acceleration since an additional forward-directed force acts on the
CG. Conversely, in order to achieve acceleration (or deceleration)
of the transporter, additional leaning (forward or backward) must
be provided in a manner discussed in further detail below.
[0042] FIG. 1 shows a simplified embodiment of the invention. A
personal transporter is shown and designated generally by numeral
18. A subject 10 stands on a support platform 12 and holds a grip
14 on a handle 16 attached to the platform 12, so that the
transporter 18 of this embodiment may be operated in a manner
analogous to a scooter. A control loop may be provided so that
leaning of the subject results in the application of torque to
wheel 20 about axle 22 thereby causing an acceleration of the
transporter. Transporter 18, however, is statically unstable, and,
absent operation of the control loop to maintain dynamic stability,
subject 10 will no longer be supported in a standing position and
will fall from platform 12. Different numbers of wheels or other
ground-contacting members may advantageously be used in various
embodiments of the invention as particularly suited to varying
applications. Thus, as described in greater detail below, the
number of ground-contacting members may be any number equal to, or
greater than, one. For many applications, the dimensions of
platform 12, and indeed of the entire ground-contacting module,
designated generally by numeral 6, are advantageously comparable to
the dimensions of the footprint or shoulder width of user 10. Thus
transporter 18 may advantageously be used as a mobile work platform
or a recreational transporter such as a golf cart, or as a delivery
transporter.
[0043] Transporter 18 may be operated in a station-keeping mode,
wherein balance is maintained substantially at a specified
position. Additionally, transporter 18, which may be referred to
herein, without limitation, as a "transporter," may also maintain a
fixed position and orientation when the user 10 is not on platform
12. This mode of operation, referred to as a "kickstand" mode,
provides a convenience for the user. A force plate 8 or other
sensor, disposed on platform 12, detects the presence of a user on
the transporter.
[0044] Another embodiment of a balancing transporter in accordance
with the present invention is shown in FIG. 2 and designated
generally by numeral 24. Personal transporter 24 shares the
characteristics of transporter 18 of FIG. 1, namely a support
platform 12 for supporting subject 10 and grip 14 on handle 16
attached to platform 12, so that the transporter 18 of this
embodiment may also be operated in a manner analogous to a scooter.
FIG. 2 shows that while transporter 24 may have clusters 26 each
cluster having a plurality of wheels 28, transporter 24 remains
statically unstable and, absent operation of a control loop to
maintain dynamic stability, subject 10 will no longer be supported
in a standing position and will fall from platform 12. In the
embodiment of FIG. 2, as in the embodiment of FIG. 1, the primary
ground-contacting members are a pair of wheels. Supplemental
ground-contacting members may be used in stair climbing and
descending or in traversing other obstacles. In one mode of
operation, for example, it is possible to rotate clusters 26 so
that two wheels on each of the clusters are simultaneously in
contact with the ground. Stair climbing and flat-terrain locomotion
may both be achieved, however, with the transporter supported on
only a single set of primary ground-contacting members.
[0045] Operation of the balancing transporter will be described
with reference to the set of coordinate axes shown in FIG. 1.
Gravity defines the vertical axis z, while the axis coincident with
the wheel axis 22 may be used to define a lateral axis y, and a
fore-aft axis x is defined by the forward direction of motion of
the transporter. The plane defined by the vertical axis z and the
lateral axis y will sometimes be referred to as the "lateral
plane", and the plane defined by the fore-aft axis x and the
vertical axis z will sometimes be referred to as the "fore-aft
plane". Directions parallel to the axes x and y are called the
fore-aft and lateral directions respectively. It can be seen that
the transporter, when relying on the pair of wheels 20 for
contacting the ground, is inherently unstable with respect to a
vertical in the fore-aft direction, but is relatively stable with
respect to a vertical in the lateral direction. In other
embodiments of the invention described below, the transporter may
also be unstable with respect to yaw about the z axis.
[0046] The axes may also be defined with respect to platform 12 in
cases such as where the ground-contacting member is a uniball.
[0047] A simplified control algorithm for achieving balance in the
embodiment of the invention according to FIG. 1 when the wheels are
active for locomotion is shown in the block diagram of FIG. 3. The
plant 61 is equivalent to the equations of motion of a system with
a ground contacting module driven by a single motor, before the
control loop is applied. T identifies the wheel torque. The
remaining portion of the figure is the control used to achieve
balance. The boxes 62 and 63 indicate differentiation. To achieve
dynamic control to insure stability of the system, and to keep the
system in the neighborhood of a reference point on the surface, the
wheel torque T in this embodiment is governed by the following
simplified control equation:
[0048] T=K.sub.1(.theta.-.theta..sub.0)+K.sub.2({dot over
(.theta.)}-{dot over
(.theta.)}.sub.0)+K.sub.3(x-x.sub.0)+K.sub.4({dot over (x)}-{dot
over (x)}.sub.0) (Eqn. 4)
[0049] where:
[0050] T denotes a torque applied to a ground-contacting element
about its axis of rotation;
[0051] .theta. is a quantity corresponding to the lean of the
entire system about the ground contact, with .theta..sub.0
representing the magnitude of a system pitch offset, all as
discussed in detail below;
[0052] x identifies the fore-aft displacement along the surface
relative to a fiducial reference point, with x.sub.0 representing
the magnitude of a specified fiducial reference offset;
[0053] a dot over a character denotes a variable differentiated
with respect to time; and
[0054] a subscripted variable denotes a specified offset that may
be input into the system as described below; and
[0055] K.sub.1, K.sub.2, K.sub.3, and K.sub.4 are gain coefficients
that may be configured, either in design of the system or in
real-time, on the basis of a current operating mode and operating
conditions as well as preferences of a user. The gain coefficients
may be of a positive, negative, or zero magnitude, affecting
thereby the mode of operation of the vehicle, as discussed below.
The gains K.sub.1, K.sub.2, K.sub.3, and K.sub.4 are dependent upon
the physical parameters of the system and other effects such as
gravity. The simplified control algorithm of FIG. 3 maintains
balance and also proximity to the reference point on the surface in
the presence of disturbances such as changes to the system's center
of mass with respect to the reference point on the surface due to
body motion of the subject or contact with other persons or
objects. It should be noted that the amplifier control may be
configured to control motor current (in which case torque T is
commanded, as shown in FIG. 3) or, alternatively, the voltage
applied to the motor may be controlled, in which case the commanded
parameter is velocity.
[0056] The effect of .theta..sub.0 in the above control equation
(Eqn. 4) is to produce a specified offset .theta..sub.0 from the
non-pitched position where .theta.=0. Adjustment of .theta..sub.0
will adjust the vehicle's offset from a non-pitched position. As
discussed in further detail below, in various embodiments, pitch
offset may be adjusted by the user, for example, by means of a
thumb wheel 32, shown in FIG. 1. An adjustable pitch offset is
useful under a variety of circumstances. For example, when
operating the vehicle on an incline, it may be desirable for the
operator to stand erect with respect to gravity when the vehicle is
stationary or moving at a uniform rate. On an upward incline, a
forward torque on the wheels is required in order to keep the
wheels in place. This requires that the user push the handle
further forward, requiring that the user assume an awkward
position. Conversely, on a downward incline, the handle must be
drawn back in order to remain stationary. Under these
circumstances, .theta..sub.0 may advantageously be manually offset
to allow control with respect to a stationary pitch comfortable to
the user.
[0057] The size of K.sub.3 will determine the extent to which the
transporter will seek to return to a given location. With a
non-zero K.sub.3, the effect of x.sub.0 is to produce a specified
offset -x.sub.0 from the fiducial reference by which x is measured.
When K.sub.3 is zero, the transporter has no bias to return to a
given location. The consequence of this is that if the transporter
is caused to lean in a forward direction, the transporter will move
in a forward direction, thereby maintaining balance. Such a
configuration is discussed further below.
[0058] The term "lean" is often used with respect to a system
balanced on a single point of a perfectly rigid member. In that
case, the point (or line) of contact between the member and the
underlying surface has zero theoretical width. In that case,
furthermore, lean may refer to a quantity that expresses the
orientation with respect to the vertical (i.e., an imaginary line
passing through the center of the earth) of a line from the center
of gravity (CG) of the system through the theoretical line of
ground contact of the wheel. While recognizing, as discussed above,
that an actual ground-contacting member is not perfectly rigid, the
term "lean" is used herein in the common sense of a theoretical
limit of a rigid ground-contacting member. The term "system" refers
to all mass caused to move due to motion of the ground-contacting
elements with respect to the surface over which the transporter is
moving.
[0059] "Stability" as used in this description and in any appended
claims refers to the mechanical condition of an operating position
with respect to which the system will naturally return if the
system is perturbed away from the operating position in any
respect.
[0060] In order to accommodate two wheels instead of the one-wheel
system illustrated for simplicity in FIG. 3, separate motors may be
provided for left and right wheels of the transporter and the
torque desired from the left motor and the torque desired from the
right motor can be calculated separately in the general manner
described below in connection with FIG. 7. Additionally, tracking
both the left wheel motion and the right wheel motion permits
adjustments to be made to prevent unwanted turning of the
transporter and to account for performance variations between the
two drive motors.
[0061] In cases where gain K.sub.3 is zero, a user control input
such as a joystick may be used to adjust the torques of each motor.
The joystick has axes indicated in FIG. 4. In operation of this
embodiment, forward motion of the joystick is used to cause forward
motion of the transporter, and reverse motion of the joystick
causes backward motion of the transporter. A left turn similarly is
accomplished by leftward motion of the joystick. For a right turn,
the joystick is moved to the right. The configuration used here
permits the transporter to turn in place when the joystick is moved
to the left or to the right, by causing rotation of left and right
motors, and hence left and right wheels, at equal rates in opposite
senses of rotation. With respect to forward and reverse motion an
alternative to the joystick is simply leaning forward or backward
(in a case where K.sub.3 is zero), since the pitch sensor
(measuring .theta.) would identify a pitch change that the system
would respond to, leading to forward or reverse motion, depending
on the direction of lean. In such instances, other types of yaw
control (i.e., control to accomplish turning right or left) can be
used. Alternatively, control strategies based on fuzzy logic can be
implemented.
[0062] It can be seen that the approach of adjusting motor torques
when in the balance mode permits fore-aft stability to be achieved
without the necessity of additional stabilizing wheels or struts
(although such aids to stability may also be provided). In other
words, stability is achieved dynamically, by motion of the
components of the transporter (in this case constituting the entire
transporter) relative to the ground.
[0063] In the block diagram of FIG. 5 it can be seen that a control
system 51 is used to control the motor drives and actuators of the
embodiment of FIGS. 1-3 to achieve locomotion and balance. These
include motor drives 531 and 532 for left and right wheels
respectively. If clusters are present as in the embodiment of FIG.
2, actuators 541 and 542 for left and right clusters respectively.
The control system has data inputs including user interface 561,
pitch sensor 562 for sensing fore-aft pitch, wheel rotation sensors
563, and pitch rate sensor 564. Pitch rate and pitch may be derived
through the use of gyroscopes or inclinometers, for example, alone
or in combination. The inputs include the desired transporter pitch
theta (desired), the actual measured pitch theta, the pitch rate
thetadot, and the component of the wheel rotation velocity that is
common to the two primary wheels, omega corn. Both theta and
thetadot are typically derived from inertial sensing, as described
in U.S. Pat. No. 6,332,103, which is incorporated herein by
reference.
[0064] A grip 14 (shown in FIG. 1) may be conveniently provided
with a thumb wheel 32 (shown in FIG. 1) or thumb-operated joystick
for directional control, although other methods of control may also
be used. Thumb wheel 32 may serve multiple control purposes as will
now be described.
[0065] In accordance with other embodiments of the invention,
handle 16 and grip 14 may be absent altogether, and the platform 12
may be equipped with sensors, such as force plate 8, for example,
to detect leaning of the subject. Indeed, as described in
connection with FIG. 5 and as further described below, the pitch of
the transporter is sensed and may be used to govern operation of
the control loop, so that if the subject leans forward, the
transporter will move forward to maintain a desired velocity or to
provide desired acceleration. Accordingly, a forward lean of the
subject will cause the transporter to pitch forward and produce
forward movement; a backward lean will cause the transporter to
pitch backward and produce backward movement. Appropriate force
transducers may be provided to sense leftward and rightward leaning
and related controls provided to cause left and right turning as a
result of the sensed leaning.
[0066] Leaning may also be detected using proximity sensors.
Additionally, operation of the transporter may be governed on the
basis of the orientation of the user with respect to the
platform.
[0067] In a further embodiment, the transporter may be equipped
with a foot- (or force-) actuated switch sensitive to the presence
of a user on the transporter. Thus, for example, the transporter
may be powered automatically upon ascent of a user onto the
platform. Conversely, when the user alights from the transporter,
power can be removed and the transporter disabled. Alternatively,
the transporter may be programmed to enter a dynamic "kickstand"
mode in which the transporter remains balanced in place when the
user alights. Thus, the transporter is ready for the user to resume
travel by reboarding the transporter. Furthermore, the transporter
is thus safely parked while not actively operated by a user aboard
the transporter.
[0068] FIG. 6 is a block diagram providing detail of a driver
interface assembly 273. A peripheral microcomputer board 291
receives an input from joystick 292 as well as from inclinometer
293 or another tilt-determining arrangement. The inclinometer
provides information signals as to pitch and pitch rate. (The term
"inclinometer" as used in this context throughout this description
and in the accompanying claims means any device providing an output
indicative of pitch or pitch rate, regardless of the arrangement
used to achieve the output; if only one of the pitch and pitch rate
variables is provided as an output, the other variable can be
obtained by suitable differentiation or integration with respect to
time.) To permit controlled banking into turns by the transporter
(thereby to increase stability while turning) it is also feasible
to utilize a second inclinometer to provide information as to roll
and roll rate or, alternatively, the resultant of system weight and
centrifugal force. Other inputs 294 may also be desirably provided
as an input to the peripheral micro controller board 291. Such
other inputs may include signals gated by switches (knobs and
buttons) for platform adjustment and for determining the mode of
operation. The peripheral micro controller board 291 also has
inputs for receiving signals from the battery stack 271 as to
battery voltage, battery current, and battery temperature. The
peripheral micro controller board 291 is in communication over bus
279 with a central micro controller board that may be used to
control the wheel motors as described below in connection with FIG.
7.
[0069] FIG. 7 is a block diagram showing control algorithms,
suitable for use in conjunction with the control assemblies of FIG.
6 to provide stability for a transporter according to the
embodiment of FIGS. 1-2 and other embodiments in which the
transporter and payload are balanced on two ground-contacting
members, both during locomotion and in a fixed position. The
following conventions are used in connection with the description
below:
[0070] 1. Variables defined in world coordinates are named using a
single subscript in capital letters. World coordinates are
coordinates fixed to the earth (inertial).
[0071] 2. A non-subscripted r identifies a wheel radius.
[0072] 3. Lower case subscripts are used to indicate other
attributes, e.g., right/left, etc.: r=right; l=left; ref=reference;
f=finish; s=start.
[0073] 4. All angles are positive in the clockwise direction, where
positive travel is in the positive x direction.
[0074] 5. A dot over a variable indicates differentiation in time,
e.g., {dot over (.theta.)}.
[0075] FIG. 7 shows the control arrangement for the motors of the
right and left wheels. The arrangement has inputs of .theta., {dot
over (.theta.)}, r{dot over (.theta.)}.sub.wl (linear velocity of
the left wheel relative to the world coordinate system) and r{dot
over (.theta.)}.sub.wr (linear velocity of the right wheel), in
addition to directional inputs 3300 determined by joystick position
along X and Y axes of a reference coordinate system. Inputs
.theta., {dot over (.theta.)}, and error signals x and {dot over
(x)} (described below), subject to gains K.sub.1, K.sub.2, K.sub.3,
and K.sub.4 respectively, become inputs to summer 3319, which
produces the basic balancing torque command for the wheels, in the
general manner described above in connection with FIG. 3 above. The
output of summer 3319 is combined with the output of yaw PID loop
3316 (described below) in summer 3320, then divided in divider 3322
and limited in saturation limiter 3324, to produce the left wheel
torque command. Similarly, the output of summer 3319 is combined
with the output of PID loop 3316 in summer 3321, then divided in
divider 3323 and limited in saturation limiter 3325, to produce the
right wheel torque command.
[0076] In FIG. 7, a directional input along the X axis moves the
reference coordinate system along its X axis relative to the world
coordinate system (which represents the traveled surface), at a
velocity proportional to the displacement of the joystick. A
directional input along the Y axis rotates the reference coordinate
system about its Z axis at an angular velocity proportional to the
displacement of the joystick. It will be appreciated that motion of
the joystick in the positive X direction is here interpreted to
mean forward motion; motion of the joystick in the negative X
direction means reverse motion. Similarly, motion of the joystick
in the positive Y direction means leftward turning,
counter-clockwise as viewed from above; motion of the joystick in
the negative Y direction means rightward turning clockwise as
viewed from above. Hence the directional inputs Y and X are given
deadband via deadband blocks 3301 and 3302 respectively, to widen
the neutral position of the joystick, then subject to gains K11 and
K10, then rate-limited by limiters 3303 and 3304 respectively,
which limit the angular and linear accelerations respectively of
the reference coordinate system. The sum of these outputs achieved
through summer 3305 becomes the reference velocity {dot over
(x)}.sub.r ref whereas the difference of these outputs achieved
through summer 3306 becomes the reference velocity {dot over
(x)}.sub.l ref. These reference velocities are subtracted in
summers 3308 and 3307 from compensated linear velocity input
signals r{dot over (.theta.)}.sub.wl and r{dot over
(.theta.)}.sub.wr for left and right wheels to obtain velocity
error signals {dot over (x)}.sub.l and {dot over (x)}.sub.r for
left and right wheels within the reference coordinate system. In
turn the average of these signals, determined via summer 3317 and
divider 3318, produces a linear velocity error signal. Displacement
error signal x is derived by integrating r{dot over
(.theta.)}.sub.wl and r{dot over (.theta.)}.sub.wr in integrators
3310 and 3309, limiting the results in saturation limiters 3312 and
3311, and then averaging their outputs via summer 3313 and divider
3315. The difference between these displacements, determined via
summer 3314, produces the yaw error signal .PSI..
[0077] The yaw error signal .PSI. is run through a standard
proportional-plus-integral-plus-derivative (PID) control loop 3316,
the output of which is combined with the output of the basic
balancing torque command of summer 3319, to produce the individual
wheel torque commands, which cause the wheels to maintain fore-aft
stability and also cause the transporter to align itself with the
axes of, and follow the origin of, the reference coordinate system
as directed by directional input 3300.
[0078] Let us now consider how this control causes the transporter
to start. The directional input 3300 (which may be a joystick) will
provide a positive x for forward motion. The signal is divided and
summed in summers 3308 and 3307, and subtracted from the right and
left wheel velocity {dot over (x)}.sub.R and {dot over (x)}.sub.L
providing a negative correction; this correction leads ultimately
to a negative torque contribution at summer 3319, causing the
wheels to move backward, so as to create a torque due to gravity
that causes the transporter to lean forward. This forward lean
leads to changing .theta. and {dot over (.theta.)}, which leads to
positive corrections in summer 3319, causing the transporter to
move forward. Thus, moving the joystick forward or backward will
cause the transporter to lean forward or backward, as the case may
be, and to move in the direction of the lean. This is a property of
the control of FIG. 7. An equivalent result can be achieved by
leaning, where K.sub.3 is zero.
[0079] Acceleration of the transporter may be established by system
lean. For example, to achieve forward acceleration of the
transporter by forward system lean; the center of gravity of the
system (transporter and payload) would be placed forward of the
center of the pressure distribution of the contact region where the
wheels contact the ground--the more the lean, the more the
acceleration. Thus, furthermore, it can be seen that leaning, in
conjunction with gravity and friction, determines acceleration
(positive or negative) of the system. In this manner, if the
transporter is moving forward, pitching the system back will
achieve braking. Because the transporter must overcome friction,
there is typically some system lean when the transporter is moving
at constant velocity over level ground. In other words, looking at
the torque on the transporter caused by gravity and the torque
caused by all other external forces, the torque applied by the
motorized drive is adjusted so that the net torque from all these
sources produces a desired acceleration.
[0080] In a further embodiment of the present invention, any of the
foregoing embodiments of a transporter in accordance with the
present invention may be provided with wheel torque, T, controlled
according to Eqn. 5, which is a modified version of Eqn. 4.
T=K.sub.1(.theta.-.theta..sub.0)+K.sub.2({dot over (.theta.)}-{dot
over (.theta.)}.sub.0)+K.sub.3(x+x.sub.0)+K.sub.4{dot over (x)}
(Eqn. 5).
[0081] where
[0082] K.sub.1=K.sub.1' when the pitch angle offset,
.theta.-.theta..sub.0, is greater than or equal to zero;
[0083] K.sub.1=K.sub.1" when the pitch angle offset,
.theta.-.theta..sub.0, is less than zero;
[0084] K.sub.2=K.sub.2" when the pitch rate offset, {dot over
(.theta.)}-{dot over (.theta.)}.sub.0, is greater than or equal to
zero;
[0085] K.sub.2=K.sub.2' when the pitch angle offset, {dot over
(.theta.)}-{dot over (.theta.)}.sub.0, is less than zero;
[0086] {dot over (.theta.)}.sub.0 represents the magnitude of a
system pitch rate offset. Other definitions are as for Eqn. 4.
[0087] The gain coefficients, K.sub.1', K.sub.1", K.sub.2', and
K.sub.2" may be configured, either in design of the system or in
real-time, on the basis of a current operating mode and operating
conditions as well as preferences of a user. When gains
K.sub.1'=K.sub.1" and K.sub.2'=K.sub.2" and the system pitch rate
offset, {dot over (.theta.)}.sub.0, is zero, Eqn. 5 simplifies to
Eqn. 4.
[0088] The separation of gains K.sub.i' and K.sub.i", where i=1, 2,
in Eqn. 5 allows the response of the transporter to be tailored,
for example, to rider preferences. For example, setting gain
K.sub.1">K.sub.1' makes the transporter more responsive to
changes in pitch that are aft of the pitch offset angle than pitch
changes that are forward of this angle. Control of the transporter
in this fashion may be advantageous, allowing a rider more
(negative) acceleration with the same degree of lean in the aft
direction than would be produced by a similar lean in the forward
direction. Thus, this arrangement advantageously allows more
responsive braking than acceleration in the forward direction. Note
that Eqn. 5 allows the contributions from the separate gains to
change smoothly since the terms .theta.-.theta..sub.0 and {dot over
(.theta.)}-{dot over (.theta.)}.sub.0 are zero when the
corresponding gains switches from one value to the other.
[0089] Any of K.sub.1', K.sub.1", K.sub.2', and K.sub.2" may vary
as a function of .theta. and {dot over (.theta.)}. This function
may be non-linear. For example, if K.sub.1' and K.sub.1" are each
zero for
.theta..sub.0-.theta..sub.d.ltoreq..theta..ltoreq..theta..sub.0+.theta..s-
ub.d and non-zero otherwise, as illustrated in FIG. 9A, then a
"deadband" has been introduced about .theta.=.theta..sub.0. Changes
of pitch angle in this zone will not cause additional net torque to
be applied to the transporter. This arrangement will advantageously
widen the "neutral" zone about .theta.=.theta..sub.0. Likewise, if
K.sub.1' and K.sub.1" are as pictured in FIG. 9B, where the
magnitude of K.sub.1 is always non-zero, then a net torque will
always be applied to the transporter to compensate for
friction.
[0090] Eqn. 5 may be recast in terms of the voltage applied to the
drive of an electric motor to produce an output torque. The drive
need not be electric and some value other than torque or voltage
may be used in control of the transporter, according to a control
equation similar to Eqn. 5. All such embodiments are within the
scope of the invention.
[0091] The described embodiments of the invention are intended to
be merely exemplary and numerous variations and modifications will
be apparent to those skilled in the art. All such variations and
modifications are intended to be within the scope of the present
invention as defined in the appended claims.
* * * * *